Related papers: Maximal regularity and optimal control for a non-l…
In this work, we analyze a diffuse-interface model for tumor growth, subject to multiplicative white noises, posed on a bounded domain $\mathcal{O} \subset \mathbb{R}^d$, $d=2,3$. The model couples a stochastic incompressible convective…
During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time,…
This paper presents a model for tumor growth using nonlocal velocity. We establish some results on the existence and uniqueness of the solution for a nonlocal tumor growth model. Many experiences show that tumor spheroid can be invariant by…
This work presents a new mathematical model to depict the effect of obesity on cancerous tumor growth when chemotherapy as well as immunotherapy have been administered. We consider an optimal control problem to destroy the tumor population…
We study a time-fractional Fisher-KPP equation involving a Riemann-Liouville fractional derivative acting on the diffusion term, as derived by Angstmann and Henry (Entropy, 22:1035, 2020). The model captures memory effects in diffusive…
The availability of cancer measurements over time enables the personalised assessment of tumour growth and therapeutic response dynamics. However, many tumours are treated after diagnosis without collecting longitudinal data, and cancer…
We present and analyze new multi-species phase-field mathematical models of tumor growth and ECM invasion. The local and nonlocal mathematical models describe the evolution of volume fractions of tumor cells, viable cells (proliferative and…
Theoretical and computational tools that can be used in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth is desired. To develop such a predictive model, one must…
We propose a mathematical model for the growth and treatment dynamics of Undifferentiated Pleomorphic Sarcoma (UPS) based on a system of nonlinear differential equations. The model integrates Gompertz-type tumor growth with surface-area…
We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn--Hilliard--Darcy system coupled with an elliptic reaction-diffusion equation. The Darcy law gives rise to an elliptic equation for the…
In this work, we present a coupled 3D-1D model of solid tumor growth within a dynamically changing vascular network to facilitate realistic simulations of angiogenesis. Additionally, the model includes erosion of the extracellular matrix,…
In this paper we study the optimal control of an initial-boundary value problem for the classical nonviscous Cahn-Hilliard system with zero Neumann boundary conditions. Phase field systems of this type govern the evolution of diffusive…
In the paper we investigate a mathematical model describing the growth of tumor in the presence of immune response of a host organism. The dynamics of tumor and immune cells is based on the generic Michaelis-Menten kinetics depicting…
This paper investigates the optimal control problem for a class of parabolic equations where the diffusion coefficient is influenced by a control function acting nonlocally. Specifically, we consider the optimization of a cost functional…
We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider…
We study the growth of a periodic pattern in one dimension for a model of spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on the intermediate region, where the non-linearity cannot be negected anymore, and before…
Recent clinical trials have shown that the adaptive drug therapy can be more efficient than a standard MTD-based policy in treatment of cancer patients. The adaptive therapy paradigm is not based on a preset schedule; instead, the doses are…
In this paper, we study a nonlinearly coupled initial-boundary value problem describing the evolution of brain tumor growth including lactate metabolism. In our modeling approach, we also take into account the viscoelastic properties of the…
In this article, the feasibility of using optimal control theory will be studied to develop control theoretic methods for personalized treatment of HCV patients. The mathematical model for HCV progression includes compartments for healthy…
In the present article we demonstrate a new hybrid model of tumor growth. Our model is stochastic by tumor population development and strongly deterministic in cell motility dynamics and spatial propagation. In addition, it has excellent…